Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.3 - Polynomials and Polynomial Functions - Graphing Calculator Explorations - Page 278: 2

Answer

$-15x^3+3x^2+3x+2$

Work Step by Step

Removing the parenthesis and then combining like terms, the given expression, $ (-14x^3-x+2)+(-x^3+3x^2+4x) ,$ is equivalent to \begin{array}{l}\require{cancel} -14x^3-x+2-x^3+3x^2+4x \\= (-14x^3-x^3)+3x^2+(-x+4x)+2 \\= -15x^3+3x^2+3x+2 .\end{array} Let \begin{array}{l}\require{cancel}Y_1= (-14x^3-x+2)+(-x^3+3x^2+4x) ,\\Y_2= -15x^3+3x^2+3x+2 .\end{array} Using a graphing calculator, the graphs of $Y_1$ (dotted graph) and $Y_2$ (solid graph) are shown below. Since the graphs overlap, then $Y_2$ is the correct simplification of $Y_1.$
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